Mistake 1: Forgetting the chain rule d/dx(sin(3x)) = 3cos(3x), NOT cos(3x). The inner derivative must be included.

Mistake 2: Power rule for variable exponents d/dx(x^(sin x)) ≠ sin(x) * x^(sin x - 1). Use logarithmic differentiation instead. Correct: x^(sin x) * [cos x * ln x + sin x / x]

Mistake 3: Wrong second derivative in parametric form d^2y/dx^2 ≠ (d^2y/dt^2)/(d^2x/dt^2). Correct: [d/dt(dy/dx)]/(dx/dt).

Mistake 4: Domain errors in inverse trig simplification sin^(-1)(sin(2t)) = 2t only when -pi/2 <= 2t <= pi/2. For 2t > pi/2, it equals pi - 2t.

Mistake 5: Forgetting |x| in sec^(-1) derivative d/dx(sec^(-1) x) = 1/(|x|sqrt(x^2-1)), not 1/(xsqrt(x^2-1)). The absolute value matters for negative x.

Mistake 6: Confusing d/dx and d/dt In parametric problems, always clearly track which variable you're differentiating with respect to.